Reducing Inductive Definitions to Propositional Satisfiability

Pelov, Nikolay; Ternovska, Eugenia

doi:10.1007/11562931_18

Cited by 16 publications

(16 citation statements)

References 13 publications

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“…We have compared MidL to Smodels [21] and idsat(zChaff) [23,30]. We have thus a representative for each of the three approaches mentioned in Section 1.…”

Section: Resultsmentioning

confidence: 99%

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Satisfiability Checking for PC(ID)

Mariën

Mitra

Denecker

et al. 2005

Logic for Programming, Artificial Intelligence, and Reasoning

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The logic FO(ID) extends classical first order logic with inductive definitions. This paper studies the satisifiability problem for PC(ID), its propositional fragment. We develop a framework for model generation in this logic, present an algorithm and prove its correctness. As FO(ID) is an integration of classical logic and logic programming, our algorithm integrates techniques from SAT and ASP. We report on a prototype system, called MidL, experimentally validating our approach.

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“…We have compared MidL to Smodels [21] and idsat(zChaff) [23,30]. We have thus a representative for each of the three approaches mentioned in Section 1.…”

Section: Resultsmentioning

confidence: 99%

“…We have chosen for a direct implementation, in contrast to a mapping to ASP, or to propositional logic, as was done in [23]. The latter approach is similar to ASP systems such as ASSAT [14] and Cmodels [13].…”

Section: Conclusion Related and Future Workmentioning

confidence: 99%

Satisfiability Checking for PC(ID)

Mariën

Mitra

Denecker

et al. 2005

Logic for Programming, Artificial Intelligence, and Reasoning

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“…. For instance, the languages considered in [19] have nonclassical negation but not classical negation, which is enough to define the class of general logic programs, and studies the relationships between four possible semantics; [1,7,10,28,30,26,16], is a very small selection of the many other studies that study the expressive power of various underlying languages, the semantics of various classes of logic programs and their relationships, and the possible equivalences between logic programs. The language of logic programs adopted in this paper is apparently a generalisation of the language of general logic programs as its only form of negation is classical, but it accepts countable disjunctions and conjunctions in the bodies of the rules (see [14] for another study where infinitary formulas are also allowed), arbitrary quantification, and a notion of identity of terms.…”

Section: Can_fly(x) ← Bird(x) Not¬can_fly(x)mentioning

confidence: 99%

Logic programming as classical inference

Martin

2015

Journal of Applied Logic

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We propose a denotational semantics for logic programming based on a classical notion of logical consequence which is apt to capture the main proposed semantics of logic programs. In other words, we show that any of those semantics can be viewed as a relation of the form T |= X where T is a theory which naturally represents the logic program under consideration together with a set of formulas playing the role of "hypotheses", in a way which is dictated by that semantics, |= is a notion of logical consequence which is classical because negation, disjunction and existential quantification receive their classical meaning, and X represents what can be inferred from the logic program, or an intended interpretation of that logic program (such as an answer-set, its well-founded model, etc.). The logical setting we propose extends the language of classical modal logic as it deals with modal operators indexed by ordinals. We make use of two kinds of basic modal formulas: 2 α ϕ which intuitively means that the logical program can generate ϕ by stage α of the generation process, and 3 α 2 β ϕ with α > β, which intuitively means that ϕ can be used as a hypothesis from stage β of the generation process onwards, possibly expecting to confirm ϕ by stage α (so expecting 2 α ϕ to be generated). This allows us to capture Rondogiannis and Wadge's version of the well-founded semantics [27] where a member of the well-founded model is a closed atom which receives an ordinal truth value of true α or false α for some ordinal α: in our framework, this corresponds to having T |= 2 α ϕ or T |= 2 α ¬ϕ, respectively, with T being the natural representation of the logic program under consideration and the right set of "hypotheses" as dictated by the well-founded semantics. The framework we present goes much beyond the proposed traditional semantics for logic programming, as it can for instance let us investigate under which conditions a set of hypotheses can be minimal, with each hypothesis being activated as late as possible and confirmed as soon as possible, setting the theoretical foundation to sophisticated ways of making local use of hypotheses in knowledge-based systems, while still being theoretically grounded in a classical notion of logical consequence.

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“…Copris was included in order to provide an idea how modern CSP-to-SAT techniques fare with respect to SPEC2SAT. However, there are some crucial differences between the language accepted by copris and NP-SPEC, most importantly the apparent absence of language features supporting inductive definitions in copris (provided by Datalog rules in NP-SPEC; techniques introduced in (Pelov & Ternovska, 2005;Mariën, Wittocx, Denecker, & Bruynooghe, 2008) may be used for this purpose, but are not the objective of this paper). On the other hand, SPEC2SAT also does not support recursive predicate definitions in the NP-SPEC input (but NPSPEC2ASP does).…”

Section: Benchmarks From the 3rd And 4th Asp Competitionsmentioning

confidence: 99%

Effectively solving NP-SPEC encodings by translation to ASP

Alviano

Faber

2015

Journal of Experimental & Theoretical Artificial Intelligen

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NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECL i P S e Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into ASP, and provide an experimental evaluation of existing implementations and the proposed translations to ASP using various ASP solvers. The results show that translating to ASP clearly has an edge over the existing translation into SAT, which involves an intrinsic grounding process. We also argue that it might be useful to incorporate certain language constructs of NP-SPEC into mainstream ASP.

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Reducing Inductive Definitions to Propositional Satisfiability

Cited by 16 publications

References 13 publications

Satisfiability Checking for PC(ID)

Satisfiability Checking for PC(ID)

Logic programming as classical inference

Effectively solving NP-SPEC encodings by translation to ASP

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